It seems as though "nice" spaces don't have torsion in their homology groups. What is the underlying characteristic of these nice spaces; that they can be embedded in $\mathbb{R}^3$? So what are some ...

I am studying Reshetikhin-Turaev TQFT. In their paper or in the book " Quantum invariants of knots and 3-manifolds", they first define an invariant $\tau(M)$ for a closed orientable 3-manifold $M$ and ...

I am currently trying to read Quillen's Cobordism paper - On the formal group laws of unoriented and complex cobordism theory Bull. Amer. Math. Soc, 75 (1969) pp. 1293–1298. Still on the first page ...

Ok, this is a major rewriting of my previous entry which no one answered.
Let us have two graded $F[t]$-modules M and N with bases $m_1, \ldots, m_m$
and $n_1, \ldots, n_n$, respectively, and $F$ is ...

Can someone point me to a rigorous definition of a connected sum of two smooth embeddings? I know about the usual construction, the problem is that I can't find a proof that this construction is well ...

Let $R$ be a ring, and let $I = (x_0,\ldots,x_{n-1})$ be a finitely-generated ideal inside of $R$, generated by a regular sequence.
In algebraic topology one often encounters a ring, usually denoted ...

I'm looking for a good update reference covering the material in first three chapters of "Adams, Infinite loop spaces" (specially construction of delooping functors and group completion) with exact ...

Let $X$ be a surface of infinite genus that is not compact (with edges extending to infinity). How would I show that this is a covering space of the 2-torus $T^{1}\# T^{1}$ via the action of the free ...

Let $f,g:C_\bullet \rightarrow D_\bullet$ be chain maps. Let $T$ be a generator (possibly not the only one) of $C_n$ and assume $H_n(C)=0$. I'm trying to prove that for every $T$ there's a solution ...

I know that $\pi_n(U(n)) \cong \mathbb{Z}$ for $n$ odd. I am looking for a description of an explicit map $S^n \rightarrow U(n)$ that represents the generator in this group. By precomposing with maps ...

Suppose $X$ is an $n$-dimensional regular CW-space (a space with a regular CW decomposition). What are the weakest sufficient conditions required on $X$ to ensure that all regular CW decompositions ...

I am trying to understand the topological behaviour of foliations around irreducible singularities, specially in the case of singularities in the Poincaré domain. I am using the third chapter of this ...

I am trying to find out how a $(p,n-p)$ surgery affects the Euler Characteristic of an orientable, $n-$ dimensional, compact manifold. Call the initial manifold $M$ and the post-op manifold $M'$. This ...

what is the homology group for The quotient space of $S^1 \times S^1$ obtained by identifying points in the circle $S1 \times\{x_0\} $
that differ by $\frac{2 \pi}{m}$ rotation and identifying points ...